Charge conservation as a concomitant of conformal motions coupled to generalized gauge transformations

Abstract

By using a Lagrangian for an electromagnetic field with sources (in which the four-current is assumed to be specifiable without consideration of any dependence upon a fundamental charge carrying field) we have established that in any conformally flat space–time (which includes Minkowski space–time) charge conservation may be obtained as a concomitant of infinitesimal Noether symmetry mappings that are not gauge transformations of the second kind. These Noether mappings, which couple geometrical and internal symmetries, are a combination of point mappings which define conformal motions in space–time with associated generalized gauge transformations of the four-vector potential.